Due to the broadcast nature of wireless communications systems, such as spread spectrum communications, radar, mobile device communications, etc., communicating devices need to differentiate between and/or synchronize with signals being transmitted by other devices in a given proximity. In addition, where the transmitting device is also receiving its signal, it needs to differentiate that signal from other signals. This can be accomplished by applying polyphase sequences to transmit signals, applying the sequences as communications preambles or headers for timing synchronization and channel estimation, and/or the like. Some polyphase sequences, more specifically constant amplitude zero autocorrelation (CAZAC) sequences, have evolved including Frank sequences, which are constrained to square numbered lengths, and Chu sequences, which are constrained to prime numbered lengths, when pairwise cross correlation properties need to be optimal.
Designed polyphase sequences can be application specific, for example. For radar, a utilized polyphase sequence exhibiting low sidelobe energy can be desired. Merit factors and/or peak-to-side-peak ratios can be utilized to measure total sidelobe energy and/or peak sidelobe energy. Chu and Frank sequences have tolerable merit factors and peak-to-side-peak ratios, and thus are used in implementations currently; however, Frank sequences are severely limited in available lengths, and Chu sequences require larger alphabet sizes to achieve desirable sidelobe energy. In addition, improved implementations seek to raise Frank sequence merit factors to more desirable levels, but do so at the cost of further increasing alphabet size. However, increased alphabet sizes typically lead to increased system implementation cost.